At the zero lower bound on safe nominal short-term interest rates, an expansionary fiscal policy impetus of d percent of current GDP will:
- raise current output by (μ)d,
- raise future output by (φμ)d, and
- raise the debt to GDP ratio by a proportional amount ΔD = (1 - μτ - μφ)d,
where μ is the Keynesian multiplier, τ is the tax rate, and φ is the hysteresis coefficient.